Spherical Micelles and Other Self-Assembled Structures in Dilute

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J. Phys. Chem. B 2001, 105, 8420-8430

Spherical Micelles and Other Self-Assembled Structures in Dilute Aqueous Mixtures of Poly(Ethylene Glycol) Lipids Markus Johnsson,* Per Hansson, and Katarina Edwards Department of Physical Chemistry, Uppsala UniVersity, P.O. Box 532, S-75121 Uppsala, Sweden ReceiVed: March 22, 2001; In Final Form: June 27, 2001

In this work we report on the characteristics of dilute mixtures of poly(ethylene glycol) derivatized lipids (PEG lipids) in aqueous solution. We show that for PEG lipids with PEG of molecular weight 750, 2000, and 5000 covalently coupled to DSPE (distearoyl phosphatidylethanolamine), spherical micelles are formed. The hydrodynamic radii and aggregation numbers of the micelles are determined as a function of temperature. The hydrodynamic thickness of the polymer layer is also determined, and the experimental values are compared with theoretically predicted values using a starlike polymer scaling model. We show a quantitative agreement between the experimental and theoretically predicted values. The phospholipid anchor carries a negative charge, and the surface potential of the micelles is estimated using a fluorescent probe titration technique. The experimental values are compared with values of the surface potential calculated using a program that solves the Poisson-Boltzmann equation numerically for the spherical geometry. A reasonable agreement between the experiments and the calculations is found. Based on the range of the electrostatic interaction, we infer that the steric repulsion caused by the overlap of the polymeric coronas dominates the intermicellar interactions. In addition to spherical micelles, we also observe some interesting aggregates in samples containing PEG(750)-DSPE which are found to be of lamellar character. For the PEG(2000) and PEG(5000) lipids no lamellar aggregates are observed, but it is found that micellar solutions of these lipids are only metastable at temperatures below approximately 60 °C.

Introduction Poly(ethylene glycol) (PEG) derivatized lipids (PEG lipids) are extensively used for the steric stabilization of liposomes (vesicles).1-3 Upon incorporation of an appropriate amount of PEG lipids in the membrane, the colloidal stability of the liposomes is increased severalfold. Thus, the tendency of conventional liposomes to aggregate with subsequent sedimentation is largely avoided. This stabilization has also been found to be very useful for the application of liposomes in drug delivery, and sterically stabilized liposomes exhibit prolonged circulation in the blood stream.2,3 A relatively large number of studies dealing with the phase behavior of PEG lipid/phospholipid systems have been published.4-7 The results obtained in these studies have indeed answered some of the questions related to the efficacy of the sterically stabilized liposomes in vivo. For example, it is now known why the best in vivo results are obtained within a specific PEG lipid concentration interval. For the PEG(2000) lipid (where 2000 denotes the PEG molecular weight), this concentration interval is between approximately 4 and 10 mol %. At 4 mol %, the polymer layer is in, or close to, the so-called brush regime,8,9 thus providing a sufficiently high repulsive force against approaching macromolecules. Above 10 mol %, there is a breakdown of the liposome structure into bilayer disks and/ or micellar aggregates.6,7 Despite the fact that PEG lipids are extensively used in liposome preparations, there are surprisingly few reports on the phase behavior and aggregate structure in neat PEG lipid * To whom correspondence should be [email protected]. Fax: 46-18-508542.

addressed.

E-mail:

systems. It is generally accepted that PEG lipids form spherical micelles in dilute aqueous solution and that the critical micellar concentration of these compounds is low, on the order of a few µM (this, of course, depends on the nature of the lipid anchor).4,6,10-12 However, the available data are not entirely consistent, and there are studies reporting that PEG lipids form lamellar phases at low to moderate temperatures.1 For PEG lipids with low molecular weight PEG, such as PEG(350)-DSPE (distearoyl phosphatidylethanolamine), it has been unambiguously shown that a lamellar phase is formed in dilute aqueous solution.4 In the present study, we set out to characterize the aggregates formed in the dilute regime of the pseudo-binary systems 150 mM NaCl/PEG(X)-DSPE, where the molecular weight of the PEG headgroup, X, is 750, 2000, or 5000. A combination of experimental techniques, including light scattering and timeresolved fluorescence quenching, was employed for the investigation. The results allow us to determine the aggregation numbers and hydrodynamic radii of the PEG lipid micelles as a function of temperature. In addition to spherical micelles, we observed some interesting aggregates of lamellar character in samples containing PEG(750)-DSPE. For PEG(2000)-DSPE or PEG(5000)-DSPE, no lamellar aggregates were observed but it was found that micellar solutions of these lipids are metastable at temperatures below approximately 60 °C. Prolonged storage of the micellar solutions at 25 °C results in precipitate formation. Since the PEG lipids used in the present study are negatively charged, it is of interest to estimate the surface potential of the micelles. Thus, we have calculated the surface potential using a computer program that solves the Poisson-Boltzmann equation for a specified aggregate geometry and salt concentration.

10.1021/jp011088l CCC: $20.00 © 2001 American Chemical Society Published on Web 08/11/2001

Self-Assembled Structures in PEG Lipids The calculated values are compared with experimental values obtained from probe-titration experiments. For normal ionic micelles, the electrostatic interaction is the dominating repulsive component in the intermicellar interactions.13 However, in the present case, the micelles possess a polymeric corona, and, in addition to the electrostatic double layer repulsion, the intermicellar repulsive forces are expected to include also a steric repulsion. To obtain information about the range of the repulsive interaction caused by the overlap of the polymeric coronas, we determine the polymer layer thickness. The experimental values of the polymer layer thickness are compared with theoretically predicted values that are obtained using a starlike polymer scaling model.14 We find that the experimental values are in quantitative agreement with the theoretically predicted values. Experimental Section Materials. Poly(ethylene glycol) lipids (PEG lipids), with PEG of molar mass 750, 2000, and 5000, covalently linked via a carbamate linkage to 1,2-distearoyl-sn-glycero-3-phosphatidylethanolamine (DSPE), were purchased from Avanti Polar Lipids, Alabaster, Al. The PEG lipids were obtained as a sodium salt, and the negative charge is localized on the phosphate group. Triton X-100 was obtained from Fluka, Stockholm, Sweden. 4-Heptadecyl-7-hydroxycoumarin (HC) was obtained from Molecular Probes, Leiden, The Netherlands. Pyrene and dimethylbenzophenon (DMBP) were obtained from Sigma-Aldrich, Stockholm, Sweden. All salts and reagents were used as received. Sample Preparation. Stock solutions were prepared by adding carefully weighed amounts of PEG lipids to volumetric flasks. A solution of 150 mM NaCl, prepared in purified water (Milli-Q) was added, and the flasks were incubated at 60-70 °C for at least 3 h. This incubation was found to be necessary to obtain optically clear solutions. After cooling, the flasks were filled to the mark with 150 mM NaCl. The concentration of PEG lipid in the samples was in general between 1 and 20 mg/ mL. Such stock solutions were either used directly, after filtration (0.2-µm Anotop 10 filter, Whatman, Maidstone, U.K.), for light scattering, ultra centrifugation and c-TEM experiments, or were diluted with 150 mM NaCl for fluorescence measurements. It is important to emphasize that prolonged storage of samples containing PEG(2000) lipid or PEG(5000) lipid at 25 °C resulted in precipitate formation. Thus, only freshly prepared solutions of these PEG lipids were used in the measurements. Fluorescence Measurements. For the measurements of critical micellar concentration, a stock solution of pyrene in ethanol was added to cylindrical glass tubes. The ethanol was evaporated by a stream of nitrogen and thereafter under vacuum for 1 h. Various amounts of PEG lipid stock solution and 150 mM NaCl were added to the tubes to give a final volume of 2 mL and a final pyrene concentration of 0.5 µM. The samples were incubated in the dark at 50 °C for 24 h and at 25 °C for 24 h, with intermittent vigorous mixing. Fluorescence spectra were recorded on a SPEX-fluorolog 1650 0.22-m double spectrometer (SPEX Industries Inc., Edison, NJ) using λex ) 320 nm and λem ) 350-450 nm. Slit-widths were set to 1 mm and the temperature was controlled by means of a water-jacketed cuvette holder connected to a thermostat. At elevated temperatures, the samples were allowed to equilibrate for at least 1 h before the measurements. The surface potential Ψ0 of the micelles was determined by a probe titration method essentially as described by Fernandez and Fromherz.15 In short, this method relies on the appropriate choice of a neutral reference surface (micelle). In our case, we

J. Phys. Chem. B, Vol. 105, No. 35, 2001 8421 chose to use Triton X-100 micelles. These micelles were used in the original paper15 and should be appropriate since Triton X-100 contains a PEG headgroup (approximately 10 EO-units). Theoretically, the apparent shift of the pKa of a pH indicator when associated with a negatively charged micelle, as compared to that of a neutral micelle, is related to the elevated proton concentration at the surface of the charged micelle. Assuming that the difference of the apparent pKa between the charged micelle and the neutral reference micelle has its only origin in the electrostatic surface potential, the following relation can be used to determine Ψ0

∆pKa ) pKca - pK0a ) -FΨ0/2.303RT

(1)

where pKca and pK0a are the apparent pKa of the indicator at the interface of the charged micelle and the neutral micelle, respectively. F is the Faraday constant, R is the gas constant and T is the absolute temperature. The PEG lipid samples (1 mM) were prepared as above with the addition of 2 mM Tris as buffering substance. A small aliquot of a stock solution of HC (pH indicator) in methanol was added to the PEG lipid samples. The solutions were then equilibrated at 70 °C for 0.5 h and at 25 °C for 0.5 h. The final solutions contained a PEG lipid-to-probe ratio of ∼200 and a concentration of methanol of 0.8% (v/v). The buffered solutions were titrated to pH 12 where the acid form of HC can be neglected. The degree of dissociation was determined using the SPEX-fluorolog with λex) 366 nm and λem) 455 nm. At these wavelengths, only the base contributes to the fluorescence.15 Slit widths were set to 1 mm and the temperature was 25 °C. The pH was adjusted with acid (HCl(aq)) and measured with a 744 pH Meter (Metrohm, Sweden). Time-Resolved Fluorescence Quenching. Stock solutions of pyrene and DMBP (quencher) in ethanol were evaporated and redissolved in a stock solution of PEG(750) lipid, prepared as above (4.18 mM). The samples contained a pyrene concentration of 1.2 µM, and the quencher concentration was adjusted to the required values. Equilibration of the samples was achieved by magnetic stirring for 3 days (in the dark, at room temperature). Fluorescence decay data were recorded with the single photon counting technique. The experimental setup has been described in detail elsewhere.16 The excitation wavelength was 320 nm and the emission was measured at 395 nm. All measurements were made at 25 °C and the samples were deoxygenated by bubbling nitrogen through the solutions prior to the measurements. In systems of small micelles with narrow size distributions, fluorescence decays from probes solubilized in the micelles together with quenchers are usually well described by the InfeltaTachiya kinetic model,17,18 where a Poisson-distributed quencher is assumed. By fitting the experimental curves to the kinetic model, the average number of quenchers per micelle, 〈n〉, can be extracted. The aggregation number, Na, is obtained from 〈n〉 using the relation

Na )

Cs,m 〈n〉 Cq,m

(2)

where Cs,m and Cq,m are the concentration of surfactant and quencher, respectively, present in the micelles. However, as long as the fluorescence decay is single exponential at long times, 〈n〉 can be determined without a detailed description of the intramicellar quenching kinetics. This is useful for large micelles. Since, at long time scales, only fluorescence from probes dissolved in micelles without quencher

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will contribute to the signal, the decays can be described by

Ftf∞(t) ) F(0) e-〈n〉 e-t/τ0

(3)

where F(0) is the amplitude of the decay curve and τ0 is the fluorescence lifetime in the absence of quencher. A straightforward way to determine 〈n〉 is to normalize the quenched fluorescence decays with the natural unquenched decay and plot the result as ln{F(t)/exp(-t/τ0)} vs t. The level of the constant end values, F(∞)/F(0), directly indicates the fraction of excited probes that are present in micelles without quenchers. Assuming the Poisson distribution to be valid, one then obtains

-ln

( )

F(∞) ) 〈n〉 F(0)

(4)

Static Light Scattering. Static light scattering (SLS) measurements were performed on filtrated samples (Anotope 0.2 µm, Whatman, Maidstone, UK) using a Hamatsu photoncounting device with a 3 mW He-Ne laser. The optical constant for vertically polarized light is K ) 4π2n02(dn/dc)2/NAλ4 where n0 is the solvent refractive index, dn/dc the refractive index increment, and λ is the wavelength (633 nm). The refractive index increment () 0.130, 0.134, 0.133 mL g-1 for PEG(750), PEG(2000), and PEG(5000) lipids, respectively) was measured using a differential refractometer. The dn/dc values were, within experimental error ((0.002), independent of temperature in the interval 25-60 °C. The reduced scattering intensity, Kc/Rθ, was derived where c is the concentration and Rθ is the Rayleigh ratio defined as Rθ ) Rtol(n0/ntol)2((Is - I0)/Itol). Here Rtol is the Rayleigh ratio of the reference toluene solution (1.359 × 10-3 m-1), ntol the refractive index of toluene, and Is, I0, and Itol are the intensities scattered by the solution, the solvent and toluene, respectively. The SLS data were analyzed using

Kc/Rθ ) 1/Mw + 2B2c

(6)

where q is the magnitude of the scattering vector q ) (4πns/λ) sin(θ/2), with ns the refractive index of the solution, λ the wavelength of the radiation in a vacuum and θ the scattering angle. At high dilution, D may be expressed as

D(c) ) D0(1+kdc)

D0 ) kBT/6πηRh

(7)

(8)

where kB is the Boltzmann constant and η is the viscosity of the solvent. The DLS setup was also used for static light scattering. The procedure was as described above but using Rtol ) 3.1 × 10-3 m-1 at λ ) 488 nm.21 Cryotransmission Electron Microscopy. Electron microscopy was performed with a Zeiss 902 A instrument, operating at 80 kV. The procedure has been described in detail in a recent review22 but consists in short of the following. A thin film of the sample solution was prepared within a custom built environmental chamber with controlled temperature and humidity. A drop of the solution was placed onto a copper electron microscopy grid coated with a perforated polymer film. Excess solution was removed by means of blotting with a filter paper, leaving a thin film of the solution to span the holes of the polymer film. Vitrification of the thin film was achieved by rapidly plunging the grid into liquid ethane held just above its freezing point. The vitrified specimen was thereafter transferred to the microscope. To prevent sample perturbation, the temperature was kept below 108 K during both the transfer and viewing procedures. Ultracentrifugation. Sedimentation measurements were made on samples containing PEG(2000) lipid using a MSE analytical ultracentrifuge (Centriscan 75) equipped with schlieren optics, at 50000 rpm. The measurements were made at 25 °C. The molecular weight of the micelles Ms was obtained from the following relation

Ms )

(5)

where Mw is the weight average micelle molecular weight and B2 is the second virial coefficient. All measurements were performed at one angle (θ ) 90°) because there was no angular dependence of the reduced scattering intensity. This is due to the small size of the micelles. Dynamic Light Scattering. The light scattering setup consists, as described previously,19 of an Ar ion laser emitting vertically polarized light at 488 nm. The detector optics include an ITT FW 130 photomultiplier and ALV-PM-PD amplifierdiscriminator connected to an ALV-5000 autocorrelator built into a computer. In dynamic light scattering (DLS), the intensity-intensity autocorrelation function g2(t) is measured and is related to the electric field autocorrelation g1(t), by the Siegert relation. The parameter g1(t) can be written as the Laplace transform of the distribution of the relaxation rate Γ. Such Laplace transformations were performed using a constrained regularization routine (REPES).20 From the relaxation rates, the translational diffusion coefficient D may be obtained as

D ) Γ/q2

where c is the particle concentration and kd a constant. D0 is related to the hydrodynamic radius Rh through the StokesEinstein relation

S0RT

(9)

D0(1 - Vj2F0)

where S0 is the sedimentation coefficient determined by extrapolating the data to infinite dilution, D0 is the diffusion coefficient obtained from DLS, F0 is the density of the solvent, and Vj2 is the partial specific volume. The term Vj2 was determined using a Kratky digital densimeter (Model DMA02, A. Paar, AG, Graz, Austria). Calculations of Surface Potentials. To calculate the surface potentials of the micelles, the computer program PBCell.123 was used. This program solves the Poisson-Boltzmann (PB) equation,

r0∇2Ψ ) - e

∑i zici0/ exp

( ) -zieΨ kBT

(10)

for a specified aggregate geometry and salt concentration. r is the dielectric constant (78.5 for water), 0 is the vacuum dielectric permittivity, Ψ is the electrostatic potential, e is the / electronic charge, zi is the ion valency and ci0 is the concentration of species i at zero potential. To obtain the surface potential, the area per surface charge has to be known. This was calculated for the different PEG lipid micelles as outlined in Appendix 1. Results and Discussion Critical Micelle Concentrations. The cmc values of the PEG lipids were determined using pyrene solubilization.24-28 In Figure 1, the fluorescence intensity (I1) and the characteristic

Self-Assembled Structures in PEG Lipids

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Figure 1. Pyrene fluorescence intensity (left y axis) and the characteristic I1/I3 ratio (right y axis) in samples containing PEG(2000)-DSPE. Open symbols represent data obtained at 25 °C and filled symbols represent data obtained at 40 °C. The lines going through the data points are only drawn to guide the eye. The cmc was estimated from the graph as indicated by the black arrow. The fluorescence intensity at 40 °C is multiplied by a factor 1.35.

TABLE 1: Properties and Critical Micelle Concentrations of the PEG lipids in 150 MM NaCl at 25 °C NEOa

cmcb/µM

I1/I3c

1509.95

17

1.03

PEG(2000)-DSPE

2748.07

45

PEG(5000)-DSPE

5783.11

114

4.9 (0.0074) 5.0 (0.0137) 4.8 (0.0278)

PEG lipid

molar mass

PEG(750)-DSPE

1.05 1.04

a Number of EO units (OCH CH ). b In units of mg mL-1 within 2 2 parentheses. c At high surfactant concentration (see text).

I1/I3 ratio are plotted as a function of the concentration of PEG(2000) lipid. I1 is the fluorescence intensity of the 0-0 band (λ ∼ 373 nm), and I3 (λ ∼ 383 nm) is the fluorescence intensity of the third principal vibronic band. Below the cmc, pyrene resides in water solution and the relative quantum yield is low whereas the I1/I3 ratio is relatively high, ∼1.6. Above the cmc, pyrene is dissolved in the hydrophobic interior of the micelles and the quantum yield increases dramatically, whereas the I1/I3 ratio decreases abruptly. In the present study, we have used the sudden increase in fluorescence intensity to determine the cmc, as illustrated in Figure 1. In principle, the I1/I3 ratio can also be used for determining the cmc,24 but it has been shown that the cmc values determined from the fluorescence intensity curves may be more reliable.28 A number of interesting features can be deduced from the cmc measurements. First, the cmc of the PEG lipids was essentially independent of temperature in the investigated interval (25-60 °C). This is exemplified in Figure 1 where data from the PEG(2000) lipid system at 25 and 40 °C are plotted. A similar behavior was found for the other PEG lipids (not shown). Thus, only cmc values obtained at 25 °C are displayed in Table 1. Second, the cmc was found to be, within experimental error, independent of PEG chain length (Table 1), clearly indicating that the onset of micellization is determined largely by the insoluble lipid anchor. This in line with previous studies of block copolymers28 and PEG lipids similar to those studied here.29 We note that the cmc of ∼5 µM for the PEG(2000) and PEG(5000) lipids (PEG-DSPE) is in agreement with previously

published values.10,11 Third, the I1/I3 ratios, at high surfactant concentration, were found to be between 1.03 and 1.05 (Table 1). Although the absolute magnitude of the I1/I3 ratio can depend somewhat on the experimental setup, this is considerably smaller than for polystyrene (PS)-PEG block copolymer micelles (∼1.20)26 and Triton X-100 micelles (∼1.30).24 However, the values obtained are close to those determined for anionic surfactants such as sodium laurate (∼1.04).24 The observed I1/ I3 ratios may indicate a smaller water penetration in the anionic PEG lipid micelles compared with the nonionic PS-PEG block copolymer micelles.24 Aggregation Numbers and Interparticle Interactions. Static light scattering (SLS) measurements were performed in order to obtain information about micelle molecular weight (Mw) and interparticle interactions. Some specific points have to be emphasized before we discuss the results. First, solutions containing PEG(2000) or PEG(5000) lipid displayed precipitate formation (or crystal formation) when incubated for prolonged periods at 25 °C. Thus, only freshly prepared samples of these lipids were used in the SLS investigations. Second, the samples containing PEG(750) lipid were found to contain large nonmicellar aggregates at the outset of the study. As will be shown below, these large aggregates disappeared when the samples were incubated at 70 °C for at least 3 h. Thus, samples containing the PEG(750) lipid were incubated at 70 °C before the SLS measurements. In Figure 2, the reduced scattering intensity is plotted against the concentration of the PEG lipids. In principle, the concentration should be corrected for the concentration of free monomers in solution. However, as shown above, the monomer concentration is in the order of 5 µM (Table 1) in all cases and is thus negligible. From Figure 2, where data from three different temperatures are displayed, it is apparent that the micelle molecular weight decreases with temperature for all of the PEG lipids. The determined aggregation numbers are given in Table 2 and were between 62 and 91, being somewhat larger for the PEG(750) lipid at 25 °C and 40 °C compared with the other PEG lipids. It is also clear that B2 is positive in all cases, meaning that the intermicellar interaction is repulsive. We also note that there are only small changes in B2 with temperature. B2 can also be expressed in terms of the equivalent hard sphere radius RHS according to30

[ ]

3B2 M2w RHS ) 16πNA

1/3

(11)

RHS values are given in Table 2 and ranged from 60 Å for PEG(750) lipid micelles up to 135 Å for PEG(5000) lipid micelles, at 25 °C. To get independent estimates of the aggregation numbers and to verify the results obtained in the SLS measurements, we performed time-resolved fluorescence quenching (TRFQ) measurements. This technique has been used extensively to measure aggregation numbers in surfactant systems, and theoretical treatments on TRFQ can be found elsewhere.31-34 Unfortunately, the addition of the quencher (dimethylbenzophenon, DMBP) to samples containing PEG(2000) or PEG(5000) lipid resulted in substantially increased rates of precipitation. The reason for this is not known, but a possible explanation may be that the quencher molecules nucleate crystal formation. This behavior was not found for PEG(750) lipids and thus the TRFQ measurements could be performed. Figure 3 shows typical TRFQ results using three different quencher concentrations. The

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Figure 3. Normalized fluorescence decay curves for PEG(750) lipid micelles (4.18 mM) at 25 °C and at three different quencher (Q ) DMPB) concentrations; [Q] ) 6.0 × 10-5 M (top), 8.9 × 10-5 M (middle), 1.2 × 10-4 M (bottom). The level of the constant end values is determined as indicated with the dashed lines. The arrow indicates how the ratio F(∞)/F(0) is determined graphically from the plot. The Na values are calculated to be (from top to bottom) 83, 79, and 84.

Figure 2. Reduced scattering intensity from SLS as a function of the concentration of PEG(750) lipid (a), PEG(2000) lipid (b), and PEG(5000) lipid (c). The measurements were performed at 25 °C (O), 40 °C (0), and 60 °C (4). The lines through the data points represent linear fits to the data.

TABLE 2: Data Obtained from Static Light Scattering (SLS) PEG(X)-lipid

T (°C)

Mw × 10-5

Na

B2 × 104 (mol mL g-2)

RHS (Å)

750

25 40 60 25 40 60 25 40 60

1.378 1.216 0.944 2.094 2.000 1.716 4.472 3.968 3.642

91 81 62 76 73 62 77 69 63

1.12 1.33 1.36 0.97 1.46 1.48 1.25 1.25 1.20

60 58 49 75 83 76 135 125 116

2000 5000

level of the constant end values (see eq 4) was determined graphically as shown in Figure 3. The micelle aggregation number was calculated as outlined in the Experimental Section

and was in the range of 79-84 (see also legend of Figure 3), which is in reasonable agreement with the value determined by SLS at 25 °C (Table 2). Sedimentation measurements were performed on samples containing the PEG(2000) lipid. By using the obtained sedimentation coefficient, the diffusion coefficient from DLS (see below) and the determined partial specific volume (Vj2 ) 0.854 × 10-3 m3/kg), the molecular weight of the micelles Ms was calculated according to eq 9. The obtained sedimentation value of the aggregation number was 74, which is in good agreement with the value of 76 obtained by SLS (25 °C) (see also Table 2). In summary, the aggregation numbers obtained by SLS are consistent with the values obtained by TRFQ and sedimentation measurements. Micelle Size and Structure. DLS was used to determine the size of the micelles. We start by presenting data from the PEG(750) lipid system where, as mentioned above, large aggregates were found to be present at the outset of the study. Figure 4 shows the size distribution of a sample containing 19.9 mg PEG(750) lipid/mL, at different temperatures. At low temperatures, the size distribution is clearly bimodal, while at 70 °C there is only one peak present. At 25 °C, the fast mode corresponds to aggregates with hydrodynamic radii, Rh, of ∼50 Å while the relativley broad slow mode corresponds to aggregates with hydrodynamic radii of ∼500-800 Å. The exact position of the broad slow peak varied somewhat with concentration (not shown). However, both modes shown in Figure 4 were diffusive as evidenced by the linear dependence of Γ on q2 (see eq 6) (data not shown). The above PEG(750) lipid sample was prepared by dissolving the lipid in 150 mM NaCl and incubating the solution at 50 °C for 15 min, whereafter the solution was stirred at room temperature for 12 h. Evidently, this preparation procedure was not adequate to remove the large aggregates from the solution. Therefore, all samples in the subsequent studies

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J. Phys. Chem. B, Vol. 105, No. 35, 2001 8425

Figure 4. Relaxation time distributions from DLS at different temperatures for a sample containing 19.9 mg PEG(750) lipid/mL. The scattering angle was 90°. The peaks are normalized with respect to the amplitude of the fast peak (the amplitude of the fast peak was set to 1 at all temperatures).

investigated by SLS (see above) or DLS were heated to 70 °C for at least 3 h. Cryo-transmission electron microscopy (c-TEM) was used in order to investigate the nature of the large aggregates found prior to heating above 70 °C. Samples for c-TEM were prepared as described above with a short incubation at 50 °C and thereafter incubation at room temperature for 12 h. As shown in Figure 5a, we found clear evidence that the aggregate structure was in the form of lamellar fragments (or bilayer disks). The size of the disks seems to be consistent with the size estimated from DLS. It should be mentioned, however, that the hydrodynamic radius as determined from eq 8 gives the equivalent hydrodynamic sphere radius of the disks. In addition to lamellar fragments, globular micelles can also be observed as small dark dots in the background of Figure 5a. In principle, the lamellar fragments may close up on themselves forming liposomes (vesicles). Alternatively, the fragments may grow by lateral fusion with a subsequent closing. Indeed, we found evidence of such a closing mechanism as shown in Figure 5b. It should be emphasized that the occurrence of liposomes in the c-TEM micrographs was rare. Nevertheless, the fact that liposomes do form is somewhat surprising because it is expected that the PEG headgroup should obstruct the closing or fusion of the disks.6 However, the PEG(750) headgroup is presumably too short for preventing the closing to occur. An obvious question that arises from the above results is whether the observed lamellar fragments (and liposomes) are metastable aggregates or if they reappear after cooling for sufficiently long times. To resolve this issue, we used DLS to investigate PEG(750) lipid samples stored several months (25 °C) after the heating procedure. However, the large structures did not reappear and the solution of small spherical micelles obtained after heating to 70 °C remained as such. Irrespective of whether the disklike aggregates are metastable or not, the reason behind their formation is still of interest. According to Kenworthy et al.,4 PEG(350)-DSPE forms a lamellar phase already in the dilute region of the phase diagram. If the PEG(750)-DSPE used in our study forms a lamellar phase in the more concentrated region of the phase diagram, then, if the PEG lipid is not properly mixed with the solvent, lamellar fragments may form initially. However, upon heating, the lamellar fragments are solubilized and one obtains a single

Figure 5. Cryo-TEM micrographs of samples containing 6.3 mg/mL (a) and 30.0 mg/mL (b) of PEG(750) lipid. Arrows in (a) denote disks observed edge-on (A) and face-on (B). Note also a closed liposome structure in (b). The small dark dots in the background represent spherical micelles. Bar ) 100 nm.

population of spherical micelles. Obviously, to obtain a complete picture of the above phenomenon, an investigation of the phase behavior in the more concentrated region of the phase diagram is needed. Such studies are currently being undertaken. A more trivial explanation may be that the PEG(750) lipid contains impurities that give rise to the observed aggregates. However, only one spot was found by thin-layer chromatography of the lipid, and the H1-NMR spectrum was in accordance with previously published data.35 Only a single population of relatively small aggregates was found in samples containing PEG(2000) and PEG(5000) lipid (not shown). The diffusion coefficient D was determined by plotting the results as Γ vs q2 (eq 6), yielding D as the slope of the linear fit to the data. To be able to use the Stokes-Einstein relation (eq 8), D was plotted against the particle concentration as shown in Figure 6 for the PEG(750) lipid. It may be noted that the concentration dependence of the diffusion coefficient was weak for the PEG(750) lipid micelles. A similar behavior was found also for the PEG(2000) and PEG(5000) lipid micelles (not shown). The determined hydrodynamic radii of the micelles are given in Table 3. As can be seen, Rh decreases slightly, in all cases, with increasing temperature. This is consistent with the fact that the aggregation numbers were found to decrease with increasing temperature (Table 2). Ishida et al.36 have reported that micelles of PEG(2000)-DSPE have a radius between 15 and 25 nm, whereas Lasic et al. have reported a value of 8 nm.12 The latter value agrees fairly well with our value of 6.7 nm (25 °C, Table 3). Trubetskoy and Torchilin37

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Figure 6. Concentration dependence of the diffusion coefficient in the PEG(750) lipid system. The measurements were performed at 25 °C (O), 40 °C (0), and 60 °C (4). The lines through the data points represent linear fits to the data. Figure 7. Schematic picture of the dimensions involved in the calculations of the polymer layer thickness (see text).

TABLE 3: Micelle Size and Comparison between Experimental Values of Polymer Layer Thickness with Model Predictions PEG(X)-lipid 750 2000 5000

T (°C)

D0 × 1011 (m2 s-1)

Rh (Å)

Lexp (Å)

Lcalc (Å)

Lexp/Rc

25 40 60 25 40 60 25 40 60

4.817 7.271 11.37 3.681 5.485 8.247 2.297 3.386 5.335

51 48 46 67 64 63 107 104 98

17 15 16 35 32 33 75 73 68

15 15 14 34 33 33 69 68 66

0.51 0.47 0.52 1.09 1.02 1.09 2.32 2.33 2.22

a

a The value of R was estimated as described in Appendix 1 (see c text for more information).

have reported a radius of 10 nm for PEG(5000)-EPE (egg phosphatidylethanolamine), which agrees well with our value of 10.7 nm determined for PEG(5000)-DSPE at 25 °C (Table 3). Furthermore, the Rh values were in all cases somewhat smaller than the previously calculated hard sphere radii (Table 2). However, the agreement is reasonable, thus supporting the general self-consistency of the data. Polymer Layer Thickness. To determine the polymer layer thickness the radius of the micelle core Rc must be known. Such values can be estimated using the aggregation number and the volumes of the component groups. A more detailed description of this procedure is given in Appendix 1. The relevant dimensions involved are schematically shown in Figure 7a. Using the experimentally determined Rh and the estimated Rc, the hydrodynamic layer thickness Lexp is given by

Lexp ) Rh - Rc

(12)

The Lexp values thus determined are given in Table 3. Scaling models for polymers tethered to planar surfaces have been developed by Alexander38 and de Gennes.9 The models assume a steplike density profile with all the chain ends situated on the outer side of the polymer layer. In particular, the scaling models have been shown to accurately predict the polymer layer thickness of planar polymer brushes. However, in the present study, the polymer chains are attached to a highly curved spherical core and a model that takes into account the highly

curved geometry has to be applied. The scaling analysis of such systems was first performed by Daoud and Cotton14 who showed that polymer chains tethered to small spherical cores are less stretched than polymers on planar surfaces, at equivalent polymer surface densities. In the Daoud and Cotton model (starlike model),14 it is assumed that the polymer chains do not interact with the surface, that the polymer within the tethered layer is in a semidilute regime and that this layer can be considered as several sublayers of blobs. In each of these sublayers, the blob size ζ(r) is constant and is an increasing function of r (see Figure 7b). The Daoud and Cotton model has been refined by d’Oliveira et al.39 and Vagberg et al.,40 resulting in simple analytical expressions for the polymer layer thickness. Both models have been used successfully by Farinha et al.41 to describe the polymer layer thickness in diblock copolymer (PS-PEG) micelles. In the present study, we have used the model of Vagberg et al.40 to estimate the PEG layer thickness. A more detailed description of the model can be found in Appendix 2. The final expression for the theoretical layer thickness Lcalc is

[

Lcalc ) NEOl1/V

]

V

8f(1 - V)/2V + Rc1/V - Rc 3V41/V

(13)

where NEO is the number of monomeric EO-units per chain, l is the statistical length of the monomer, V is the Flory exponent () 3/5 for a good solvent), f is the number of grafted chains which in our case is the same as the micelle aggregation number (Na) and Rc is the radius of the micelle core, estimated as described in Appendix 1. For the calculations, the values l ) 3.9 Å and V ) 0.58342 were used. These values were also used by Farinha et al. in their description of PS-PEG copolymer micelles and PS latex particles with adsorbed PS-PEG diblock copolymers.41 In Figure 8, the experimentally determined layer thickness is plotted as a function of the number of EO units in the chains. The lines represent the theoretically predicted values according to eq 13. As can be seen, the agreement between experiment and theory is good. The predicted values for the PEG(5000) lipid micelles are somewhat smaller than the experimental

Self-Assembled Structures in PEG Lipids

J. Phys. Chem. B, Vol. 105, No. 35, 2001 8427 TABLE 4: Micelle Surface Potential and Comparison between Experimental and Calculated Values PEG(X)-lipid 750 2000 5000

T (°C) 25 40 60 25 40 60 25 40 60

pKa a

Ψ0,expb (mV)

Ψ0,calcc (mV)

(eΨ/kBT) ) 1 at r ) (Å)d

9.89

-57.4

9.86

-55.6

9.87

-56.2

-84.8 -87.2 -88.1 -81.2 -85.1 -88.1 -81.5 -83.9 -88.2

6.7 6.5 6.1 6.4 6.3 6.1 6.4 6.2 6.1

a The apparent pK of HC in PEG lipid micelles. b Surface potential a determined using Triton X-100 micelles as reference micelle. c Surface potential calculated using the program PBCell.1.23 d Calculated (PBCell.1)23 distance r from the micelle surface (core surface) (see text).

Figure 8. Comparison of experimental data of the polymer layer thickness with the theoretically predicted values according to eq 13. The data points represent experimental results at 25 °C (O), 40 °C (0), and 60 °C (4). The lines represent predicted values at 25 °C (full drawn line), 40 °C (dashed line), and 60 °C (dotted line).

values. This can presumably be explained by polydispersity effects. In fact, calculations using the same parameters (V and l) for every temperature yielded values consistent with the experimental values (see also Table 3). This indicates that the solvent quality does not change appreciably for PEG (for the molecular weights studied here) within the temperature interval 25-60 °C. This is in line with the fact that the cloud point of comparably low molecular weight PEGs in water is well above 100 °C.43 It is noteworthy that even for the PEG(750) lipid micelles where the micelle core is rather large compared with the polymer layer thickness, the model is still accurate. Farinha et al. have previously found that for Lexp/Rc ratios below 0.72 the layer thickness was best described by the planar brush model, whereas for ratios above 0.72 the starlike model was the most appropriate.41 As seen in Table 3, the Lexp/Rc ratio for the PEG(750) lipid micelle was ∼0.50 and the polymer layer thickness is still well predicted by the starlike model. However, the data of Farinha et al. do not cover the whole range of possible ratios up to 0.72 and there are no results in the range 0.23 e Lexp/Rc e 0.72.41 We also note that Biver et al.44 and Hariharan et al.45 have modified the starlike model to take into account electrostatic interactions. Thereby they were able to show that also for diblock polyelectrolyte (poly(tert-butylstyrene)-sodium poly(styrenesulfonate)) micelles, or the same polymers adsorbed onto polystyrene particles, the hydrodynamic layer thickness could be described by the starlike model. Moreover, they also found that the model predicted polymer layer thickness values in reasonable agreement with experiment also at Lexp/Rc ratios below those studied here.44 Polymer scaling laws are in general not expected to be applicable for chains as short as those investigated in the present study. However, Sarmoria and Blankschtein46 have argued that scaling laws for surface grafted PEG are applicable, with good accuracy, down to 10 EO units. Polymer scaling theory has also been used by Kenworthy et al.8 to model the pressure-distance data of lipid bilayers with incorporated PEG lipid. In that study, the PEG molecular weights investigated were similar to those studied here. Furthermore, it has been shown that the micelle aggregation number of block copolymer micelles is independent of PEG chain length if the micelles conform to the starlike description.41,47 Indeed, the aggregation numbers determined in the present study are essentially independent of PEG chain

length (Table 2). In summary, the results presented above support the adequacy of using the starlike model for predicting the (hydrodynamic) layer thickness of polymers grafted or adsorbed onto spheres. Surface Potential. The surface potentials of the micelles were calculated using the computer program PBCell.1.23 This program solves the Poisson-Boltzmann equation (eq 10) numerically in an electroneutral cell for the spherical geometry and with a specified salt concentration. In the present study we chose to use a large cell such that the systems may be regarded as infinitely diluted. The area per surface charge also has to be specified, and a derivation of this parameter can be found in Appendix 1. The surface potentials obtained from the calculations Ψ0,calc are given in Table 4. The potentials are similar for the different micelles, being in the order of -80 mV at 25 °C. Importantly, the program also gives the variation of the electrostatic potential as a function of distance from the surface and we can thus determine the distance from the surface r where the parameter eΨ/kBT equals 1 (Table 4). When comparing these values with the values obtained for the polymer layer thickness (Table 3), it is clear that electrostatic interactions should be of limited importance in the intermicellar interactions. This is because it has been shown that the steric repulsive potential rises sharply when two “hairy” micelles are brought within a distance ∼2L, where L is the polymer layer thickness.48 To experimentally determine the surface potentials, we used a probe-titration method developed by Fernandez and Fromherz.15 Typical titration curves are shown in Figure 9. The determined apparent pKa of HC in neutral Triton X-100 micelles was 8.92, which corresponds well to the value of 8.85 determined by Fernandez and Fromherz.15 It is evident that the apparent pKa of the probe increases when dissolved in the PEG lipid micelles as compared to the Triton X-100 micelles. It is also clear that the apparent pKa values are very similar in all the different PEG lipid micelles, indicating similar surface potentials. This is consistent with the calculations (see also Table 4). The surface potentials were calculated using eq 1 and are given in Table 4. As can be seen, the experimentally determined values Ψ0,exp are in the order of -55 mV, which is lower than the calculated potentials (approx. -80 mV) but still in reasonable agreement. The difference between the calculated and the experimentally determined values can be due to several factors. We may consider, for example, nonelectrostatic contributions to the determined ∆pKa values, approximations in the PoissonBoltzmann model calculations,49 or a location of the fluorescent probe at the micelle surface that does not fully coincide with the location of the charges estimated in the calculations.

8428 J. Phys. Chem. B, Vol. 105, No. 35, 2001

Johnsson et al. to 2 kBT. With the above assumptions and estimations, together with the experimentally determined cmc values (Table 1), we get a free energy contribution from the PEG chains of 10-11 kBT. This value is essentially independent of the length of the PEG headgroup for the PEG lipids investigated here. Note also that the value is relatively insensitive to small experimental errors in the determination of the cmc. In any case, it is clear that the intramicellar repulsive interactions are dominated by the PEG headgroup repulsion. Concluding Remarks

Figure 9. Titration curves of HC in different micelles at 25 °C: Triton X-100 micelles (O); PEG(750) lipid micelles (9); PEG(2000) lipid micelles (b); PEG(5000) lipid micelles (2). The pKa is determined as the pH at which the dissociation degree ([B]/([B]+[A])) is 0.5. The dashed lines represent the theoretical dissociation degree, as calculated using the formula pH ) pKa + log([B]/[A]) and the experimentally determined pKa.

Regarding the latter issue, an electrostatic potential of -55 mV is obtained at a distance of ∼2 Å from the estimated micelle core surface in the calculations. Given that the calculations are correct, this indicates that the fluorescent probe headgroup is situated, on average, a small distance out from the charged surface. Free Energy of Micelle Formation. Phospholipids with long acyl chains typically have a very low monomer solubility. For example, the cmc of dipalmitoyl phosphatidylcholine (DPPC; C16 acyl chains) has been estimated to be in the order of 10-10 M.50 Obviously, in the present case, there must be a significant contribution to the intramicellar repulsive interactions (in addtion to the electrostatic repulsion) in order to reach a cmc in the 10-6 M range (Table 1). This repulsive interaction should be due to the bulky PEG headgroups. We can analyze this contribution, at least in a semiquantitative way, using the following equation for the free energy of micelle formation per PEG lipid

kBTln(cmc) ) (µ0,mic - µ0,w s s ) + µsurf + µel + µPEG

(14)

where the cmc is expressed in mole fraction units. The term within brackets includes the hydrophobic free energy contribution and can be estimated in the following way: The transfer of a double-chained alkyl part from an aqueous to a hydrophobic environment can be approximated by increasing the length of the single chain by 60% and then calculating the hydrophobic contribution.50 In the case of the PEG lipids (C17 chains, carbonyl carbon neglected), this means that we calculate the energy gain of a fictitious C27 alkyl chain. Assigning an energy 1.2 kBT to every CH2 group and 3.9 kBT to the CH3 group,32 yields a hydrophobic contribution of -35 kBT (25 °C). The next term in eq 14, µsurf, is a surface tension term which we take to be equal to a0γ, where a0 is the headgroup area (surface area per charge) calculated as shown in Appendix 1 and γ is the surface tension at the micelle hydrocarbon/water interface, which is usually found to be about 20 mJ m-2.51 The resulting surface tension term is in the order of 6 kBT in all cases. The electrostatic contribution to the free energy µel is obtained from the PBCell.123 calculations and is, for all of the PEG lipids, close

From the data in the present study it is clear that PEG(2000)DSPE and PEG(5000)-DSPE form spherical micelles in the dilute region of the phase diagram. However, to prepare these micelles, heating to above 60 °C is necessary. Prolonged storage (∼1 week) of the micelle solutions at 25 °C resulted in precipitate formation (or crystal formation), and, accordingly, the single micellar phase is not the thermodynamically stable state for these lipids at 25 °C. Previous studies have indicated that PEG lipids with comparably long PEG chains form either a single micellar phase4,6,12 or a lamellar phase.1 The reason for this discrepancy may indeed be answered by the fact that the micellar solutions are metastable and crystal formation may not have been observed in all cases. If, on the other hand, the crystals are lamellar-like, this may explain the observations by Blume and Cevc1 that PEG(5000)-DSPE forms a lamellar phase. Interestingly, Koynova et al.52 found that pure hydrated PEG(5000)-DMPE (dimyristoyl phosphatidylethanolamine) displayed a sharp SAXS reflection below 40-50 °C, which they attributed to a lamellar arrangement of the lipid. When heated, the SAXS reflection transformed into a diffuse scattering that was assumed to indicate micelle formation. They also found that this transformation was not readily reversible and the diffuse pattern was preserved upon cooling to room temperature.52 This is in accordance with the results in the present study, that is, the micelle phase is metastable at lower temperatures. Despite the above complications, we have demonstrated that the corona of the PEG lipid micelles can be described by a starlike polymer scaling model. The model accurately predicts the hydrodynamic polymer layer thickness also in the case of the PEG(750) lipid micelles, where the polymer layer is thin compared with the micelle core radius. Based on experimental and calculated values of the surface potential of the micelles, we concluded that the electrostatic intermicellar interactions should be of minor importance and that the steric interaction due to the overlap of the polymer coronas should be the dominating repulsive intermicellar interaction. Interactions between PEG headgroups also constitute the major repulsive component to the free energy of micelle formation. Acknowledgment. The authors are indebted to Mr. Go¨ran Svensk for helping us with the sedimentation measurements and to Mr. Tomas Edvinsson for many helpful discussions. Financial support from the Swedish Research Council for Engineering Sciences, the Swedish Foundation for Strategic Research, and the Swedish Cancer Foundation is gratefully acknowledged. Appendix 1 To estimate the radius of the micelle core Rc and the area per surface charge, we have used literature data of the volumes of the component groups.53 The data used were determined for LR phase lecithins, and because we are dealing with micelles in the present study, we emphasize that the Rc values are only estimates. Nevertheless, the procedure should give reasonable

Self-Assembled Structures in PEG Lipids

J. Phys. Chem. B, Vol. 105, No. 35, 2001 8429

values for the lipid anchor volume. The following component group volumes were used (in Å3):53 53.9 (CH3), 28.4 (CH2), 39.0 (carbonyl), 68.8 (glycerol), and 53.7 (phosphate). By summing up the individual group volumes and assuming a spherical shape of the micelles, the volume of the sphere Vs that includes all component groups up to the phosphate group was calculated as

Vs ) Na × 1217.1 Å3

(15)

where Na is the micelle aggregation number. The corresponding radius Rs can then be calculated from Vs. The area per surface charge As is then simply calculated as

As ) (4πRs2)/Na

(16)

While Rs gives the approximate location of the charges, the polymer is grafted to the lipid anchor a small distance away from the phosphate group (see Figure 7a). If we assume that the thickness of the lipid anchor headgroup is on the order of 8 Å and that the phosphate group is localized in the middle of that region, the total micelle core radius Rc is given by

R c ) Rs + 4 Å

(17)

Rc values calculated in this way were used in eq 13 for the model calculations of polymer layer thickness. Appendix 2 The starlike model used to predict the polymer layer thickness is due to Vagberg et al.40 From a simplified surface area match between the core and the first layer of blobs (see Figure 7b), a relationship between the blob diameter ζ(Rc), the core size Rc, and the number of tethered chains f () Na) can be obtained

ζ(Rc) ) 4 Rc f -1/2

(18)

The number of monomers in each blob Nr is given by

Nr ) (ζ(r)/l)1/V

(19)

where l is the statistical length of the monomer and V the Flory exponent. By inserting eq 18 in eq 19 and multiplying by the number of tethered chains, an expression for the total number of monomers in the first layer of blobs N(Rc) can be obtained. In a similar way, the total volume of the first layer of blobs V(Rc) is obtained. The resulting expression for the density (monomers per blob/blob volume) at the core surface becomes

F(Rc) )

3 4 1/V (1-3V) (3V-1)/2V Rc f 32π l

()

(20)

Assuming the same dependence on V along the radial distance, the density distribution of polymer segments within the polymer layer is40

F(r) ∝ r(1-3V)/V f(3V-1)/2V

(21)

where the prefactor can be determined by comparing eqs 20 and 21. The total number of monomers in the polymer layer Nf is obtained by integrating the density profile over the chain layer volume VL

∫RR c

h

F(r) dVL ) Nf

(22)

where Rh is the hydrodynamic radius. The hydrodynamic

polymer layer thickness L is obtained by solving eq 22 for Rh and subtracting the core radius, as given in eq 13. References and Notes (1) Blume, G.; Cevc, G. Biochim. Biophys. Acta 1993, 1146, 157. (2) Papahadjopoulos, D.; Allen, T. M.; Gabizon, A.; Mayhew, E.; Matthay, K.; Huang, S. K.; Lee, K.-D.; Woodle, M. C.; Lasic, D. D.; Redemann, C.; Martin, F. J. Proc. Natl. Acad. Sci. U.S.A. 1991, 88, 11460. (3) Woodle, M. C.; Lasic, D. D. Biochim. Biophys. Acta 1992, 1113, 171. (4) Kenworthy, A. K.; Simon, S. A.; McIntosh, T. J. Biophys. J. 1995, 68, 1903. (5) Hristova, K.; Kenworthy, A.; McIntosh, T. J. Macromolecules 1995, 28, 7693. (6) Edwards, K.; Johnsson, M.; Karlsson, G.; Silvander, M. Biophys. J. 1997, 73, 258. (7) Belsito, S.; Bartucci, R.; Montesano, G.; Marsh, D.; Sportelli, L. Biophys. J. 2000, 78, 1420. (8) Kenworthy, A. K.; Hristova, K.; Needham, D.; McIntosh, T. J. Biophys. J. 1995, 68, 1921. (9) de Gennes, P. G. Macromolecules 1980, 13, 1069. (10) Uster, P. S.; Allen, T. M.; Daniel, B. E.; Mendez, C. J.; Newman, M. S.; Zhu, G. Z. FEBS Lett. 1996, 386, 243. (11) Sou, K.; Endo, T.; Takeoka, S.; Tsuchida, E. Bioconjugate Chem. 2000, 11, 372. (12) Lasic, D. D.; Woodle, M. C.; Martin, F. J.; Valentincic, T. Period. Biol. 1991, 93, 287. (13) Corti, M.; Degiorgio, V. J. Phys. Chem. 1981, 85, 711. (14) Daoud, M.; Cotton, J. P. J. Phys. (Paris) 1982, 43, 531. (15) Fernandez, M. S.; Fromherz, P. J. Phys. Chem. 1977, 81, 1755. (16) Almgren, M.; Hansson, P.; Mukhtar, E.; van Stam, J. Langmuir 1992, 8, 2405. (17) Infelta, P. P.; Gra¨tzel, M.; Thomas, J. K. J. Phys. Chem. 1974, 78, 190. (18) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289. (19) Schille´n, K.; Brown, W.; Johnsen, R. M. Macromolecules 1994, 27, 4825. (20) Jakes, J. Czech. J. Phys. 1988, B38, 1305. (21) Moreels, E.; De Ceuninck, W.; Finsy, R. J. Chem. Phys. 1987, 86, 618. (22) Almgren, M.; Edwards, K.; Karlsson, G. Colloids Surf. A 2000, 174, 3. (23) Jo¨nsson, B.; The program PBCell.1 is a freeware program that can be downloaded at http://www.membfound.lth.se/chemeng1/prog.html. (24) Kalyanasundaram, K.; Thomas, J. K. J. Am. Chem. Soc. 1977, 99, 2039. (25) Dong, D. C.; Winnik, M. A. Can. J. Chem. 1984, 62, 2560. (26) Wilhelm, M.; Zhao, C.-L.; Wang, Y.; Xu, R.; Winnik, M. A.; Mura, J. -L.; Riess, G.; Croucher, M. D. Macromolecules 1991, 24, 1033. (27) Zhao, C.-L.; Winnik, M. A.; Riess, G.; Croucher, M. D. Langmuir 1990, 6, 514. (28) Astafieva, I.; Zhong, X. F.; Eisenberg, A. Macromolecules 1993, 26, 7339. (29) Takeoka, S.; Mori, K.; Ohkawa, H.; Sou, K.; Tsuchida, E. J. Am. Chem. Soc. 2000, 122, 7927. (30) Richtering, W. H.; Burchard, W.; Jahns, E.; Finkelmann, H. J. Phys. Chem. 1988, 92, 6032. (31) Almgren, M. AdV. Colloid Interface Sci. 1992, 41, 9. (32) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain: Where Physics, Chemistry, Biology and Technology Meet; VCH Publishers Inc.: New York, 1994. (33) Zana, R. In Surfactant Solutions: New Methods of InVestigation; Surfactant Science Series; Zana, R., Ed.; Marcel Dekker: New York, 1987; Vol. 22, Chapter 5. (34) Almgren, M. Kinetics and Catalysis in Microheterogeneous Systems; Gra¨tzel, M.; Kalyanasundaram, K., Eds.; Marcel Dekker: New York, 1991; Chapter 4. (35) Zalipsky, S. In Stealth Liposomes; Lasic, D.; Martin, F., Eds.; CRC Press Inc.: Boca Raton, 1995; Chapter 9. (36) Ishida, T.; Iden, D. L.; Allen, T. M. FEBS Lett. 1999, 460, 129. (37) Trubetskoy, V. S.; Torchilin, V. P. AdV. Drug Del. ReV. 1995, 16, 311. (38) Alexander, S. J. Phys. (Paris) 1977, 38, 983. (39) d’Oliveira, J. M. R.; Martinho, J. M. G.; Xu, R.; Winnik, M. A. Macromolecules 1995, 28, 4750. (40) Vagberg, L. J. M.; Cogan, K. A.; Gast, A. P. Macromolecules 1991, 24, 1670. (41) Farinha, J. P. S.; d’Oliveira, J. M. R.; Martinho, J. M. G.; Xu, R.; Winnik, M. A. Langmuir 1998, 14, 2291. (42) Devanand, K.; Selser, J. C. Macromolecules 1991, 24, 5943. (43) Saeki, S.; Kuwahara, N.; Nakata, M.; Kaneko, M. Polymer 1976, 17, 685.

8430 J. Phys. Chem. B, Vol. 105, No. 35, 2001 (44) Biver, C.; Hariharan, R.; Mays, J.; Russel, W. B. Macromolecules 1997, 30, 1787. (45) Hariharan, R.; Biver, C.; Mays, J.; Russel, W. B. Macromolecules 1998, 31, 7506. (46) Sarmoria, C.; Blankschtein, D. J. Phys. Chem. 1992, 96, 1978. (47) Willner, L.; Poppe, A.; Allgaier, J.; Monkenbusch, M.; Lindner, P.; Richter, D. Europhys. Lett. 2000, 51, 628. (48) Witten, T. A.; Pincus, P. A. Macromolecules 1986, 19, 2509. (49) In the calculations, we have assumed a dielectric constant r of 78.5. Allowing for a lower r in the interfacial region will increase the surface potential. For example, with r ) 50, Ψ0 is calculated to be approx. -98 mV (25 °C, PEG(750) lipid micelle). On the other hand, increasing the width of the micelle(core)-solution interface will tend to lower the surface potential. Both the above effects are expected to influence the

Johnsson et al. magnitude of the surface potential; however, there exists no general solution accounting for all such interfacial effects. For an extensive review on membrane electrostatics, see Cevc, G. Biochim. Biophys. Acta 1990, 1031, 311. (50) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Krieger Publishing Company: Florida, 1991. (51) Jo¨nsson, B.; Wennerstro¨m, H. J. Colloid Interface Sci. 1981, 80, 482. (52) Koynova, R.; Tenchov, B.; Rapp, G. Colloids Surf., A 1999, 149, 571. (53) Nagle, J. F.; Tristram-Nagle, S. Biochim. Biophys. Acta 2000, 1469, 159.